8.2 Comparison of Step and Disturbance Rejection Responses Figure 16 and Figure 17 show the displacement sensor output and the controller output, respectively, when a step disturbance of
Trang 18.2 Comparison of Step and Disturbance Rejection Responses
Figure 16 and Figure 17 show the displacement sensor output and the controller output,
respectively, when a step disturbance of 0.05V is applied to the channel 1 input of the
magnetic bearing system when it is controlled with the model based conventional controller
C lead (s) Note that the displacement sensor output is multiplied by a factor of 10 when it is
transmitted through the DAC
Fig 16 Displacement output of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Fig 17 Control signal of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Figure 18 and Figure 19 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.1V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the model based controller
Fig 18 Step response of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Fig 19 Control signal of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Trang 2Figure 20 and Figure 21 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the conventional controller C lead (s)
Fig 20 Step response of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Fig 21 Control signal of the MBC500 magnetic bearing system with the model based
controller C lead (s)
It can be seen from the above figures that the magnetic bearing system remain stable under the control of the model based conventional controller when a step change in disturbance of
is applied to its channel 1 input Similar results were also obtained from other channels
Figure 22 and Figure 23 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.05V is applied to the channel 1 input of the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 22 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 23 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Trang 3Figure 20 and Figure 21 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the conventional controller C lead (s)
Fig 20 Step response of the MBC500 magnetic bearing system with the model based
controller C lead (s)
Fig 21 Control signal of the MBC500 magnetic bearing system with the model based
controller C lead (s)
It can be seen from the above figures that the magnetic bearing system remain stable under the control of the model based conventional controller when a step change in disturbance of
is applied to its channel 1 input Similar results were also obtained from other channels
Figure 22 and Figure 23 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.05V is applied to the channel 1 input of the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 22 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 23 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Trang 4Figure 24 and Figure 25 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.1V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 24 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 25 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Figure 26 and Figure 27 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 26 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 27 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Trang 5Figure 24 and Figure 25 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.1V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 24 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 25 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Figure 26 and Figure 27 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of the magnetic bearing system when it is controlled with the analytical controller C 2 (s)
Fig 26 Displacement output of the MBC500 magnetic bearing system with the analytical
controller C 2 (s)
Fig 27 Control signal of the MBC500 magnetic bearing system with the analytical controller
C 2 (s)
Trang 6Figure 28 and Figure 29 show the displacement sensor output voltage and the controller
output voltage, respectively, when a step of 0.05V is applied to channel 1 of the magnetic
bearing system, when it is controlled with the FLC
Fig 28 Step response of the MBC500 magnetic bearing system with the FLC
Fig 29 Control signal of the MBC500 magnetic bearing system with the FLC
Figure 30 and Figure 31 show the displacement sensor output voltage and the controller
output voltage, respectively, when a step of 0.1V is applied to channel 1 of the magnetic
bearing system, when it is controlled with the FLC
Fig 30 Step response of the MBC500 magnetic bearing system with the FLC
Fig 31 Control signal of the MBC500 magnetic bearing system with the FLC
Trang 7Figure 28 and Figure 29 show the displacement sensor output voltage and the controller
output voltage, respectively, when a step of 0.05V is applied to channel 1 of the magnetic
bearing system, when it is controlled with the FLC
Fig 28 Step response of the MBC500 magnetic bearing system with the FLC
Fig 29 Control signal of the MBC500 magnetic bearing system with the FLC
Figure 30 and Figure 31 show the displacement sensor output voltage and the controller
output voltage, respectively, when a step of 0.1V is applied to channel 1 of the magnetic
bearing system, when it is controlled with the FLC
Fig 30 Step response of the MBC500 magnetic bearing system with the FLC
Fig 31 Control signal of the MBC500 magnetic bearing system with the FLC
Trang 8Figure 32 and Figure 33 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the FLC
Fig 32 Step response of the MBC500 magnetic bearing system with the FLC
Fig 33 Control signal of the MBC500 magnetic bearing system with the FLC
The FLC was tested extensively to ensure that it can operate in a wide range of conditions These include testing its tolerance to the resonances of the MBC500 system by tapping the rotor with screwdrivers The system remained stable throughout the whole regime of testing The MBC500 magnetic bearing system has four different channels; three of the channels were successfully stabilized with the single FLC designed without any modifications or further adjustments For the channel that failed to be robustly stabilized, the difficulty could be attributed to the strong resonances in that particular channel which have very large magnitude After some tuning to the input and output scaling values of the FLC, robust stabilization was also achieved for this difficult channel
Comparing Figures 16 and 22, 18 and 24, 20 and 26, it can be seen that the system step responses with the controller designed via analytical interpolation approach exhibit smaller overshoot and shorter settling time with similar control effort as shown in Figures 17 and 23,
19 and 25, 21 and 27 The step and step disturbance rejection responses with the designed FLC exhibit smaller steady-state error and overshoot as shown in Figures 28, 30 and 32 with much bigger control signal displayed in Figures 29, 31 and 33 However, it must be pointed out that the system stability is achieved with the designed FLC without using the two notch filters to eliminate the unwanted resonant modes
9 Conclusion and future work
In this chapter, the controller structure and performance of a conventional controller and an analytical feedback controller have been compared with those of a fuzzy logic controller (FLC) when they are applied to the MBC500 magnetic bearing system stabilization problem The conventional and the analytical feedback controller were designed on the basis of a reduced order model obtained from an identified 8th-order model of the MBC500 magnetic bearing system Since there are resonant modes that can threaten the stability of the closed-loop system, notch filters were employed to help secure stability
The FLC uses error and rate of change of error in the position of the rotor as inputs and produces an output voltage to control the current of the amplifier in the magnetic bearing system Since a model is not required in this approach, this greatly simplified the design process In addition, the FLC can stabilize the magnetic bearing system without the use of any notch filters Despite the simplicity of FLC, experimental results have shown that it produces less steady-state error and has less overshoot than its model based counterpart While the model based controllers are linear systems, it is not a surprise that their stability condition depends on the level of the disturbance This is because the magnetic bearing system is a nonlinear system However, although the FLC exhibits some of the common characteristics of high authority linear controllers (small steady-state error and amplification
of measurement noise), it does not have the low stability robustness property usually associated with such high gain controllers that we would have expected
Future work will include finding some explanations for the above unusual observation on FLC We believe the understanding achieved through attempting to address the above issue would lead to better controller design methods for active magnetic bearing systems
Trang 9Figure 32 and Figure 33 show the displacement sensor output and the controller output,
respectively, when a step change in disturbance of 0.5V is applied to the channel 1 input of
the magnetic bearing system when it is controlled with the FLC
Fig 32 Step response of the MBC500 magnetic bearing system with the FLC
Fig 33 Control signal of the MBC500 magnetic bearing system with the FLC
The FLC was tested extensively to ensure that it can operate in a wide range of conditions These include testing its tolerance to the resonances of the MBC500 system by tapping the rotor with screwdrivers The system remained stable throughout the whole regime of testing The MBC500 magnetic bearing system has four different channels; three of the channels were successfully stabilized with the single FLC designed without any modifications or further adjustments For the channel that failed to be robustly stabilized, the difficulty could be attributed to the strong resonances in that particular channel which have very large magnitude After some tuning to the input and output scaling values of the FLC, robust stabilization was also achieved for this difficult channel
Comparing Figures 16 and 22, 18 and 24, 20 and 26, it can be seen that the system step responses with the controller designed via analytical interpolation approach exhibit smaller overshoot and shorter settling time with similar control effort as shown in Figures 17 and 23,
19 and 25, 21 and 27 The step and step disturbance rejection responses with the designed FLC exhibit smaller steady-state error and overshoot as shown in Figures 28, 30 and 32 with much bigger control signal displayed in Figures 29, 31 and 33 However, it must be pointed out that the system stability is achieved with the designed FLC without using the two notch filters to eliminate the unwanted resonant modes
9 Conclusion and future work
In this chapter, the controller structure and performance of a conventional controller and an analytical feedback controller have been compared with those of a fuzzy logic controller (FLC) when they are applied to the MBC500 magnetic bearing system stabilization problem The conventional and the analytical feedback controller were designed on the basis of a reduced order model obtained from an identified 8th-order model of the MBC500 magnetic bearing system Since there are resonant modes that can threaten the stability of the closed-loop system, notch filters were employed to help secure stability
The FLC uses error and rate of change of error in the position of the rotor as inputs and produces an output voltage to control the current of the amplifier in the magnetic bearing system Since a model is not required in this approach, this greatly simplified the design process In addition, the FLC can stabilize the magnetic bearing system without the use of any notch filters Despite the simplicity of FLC, experimental results have shown that it produces less steady-state error and has less overshoot than its model based counterpart While the model based controllers are linear systems, it is not a surprise that their stability condition depends on the level of the disturbance This is because the magnetic bearing system is a nonlinear system However, although the FLC exhibits some of the common characteristics of high authority linear controllers (small steady-state error and amplification
of measurement noise), it does not have the low stability robustness property usually associated with such high gain controllers that we would have expected
Future work will include finding some explanations for the above unusual observation on FLC We believe the understanding achieved through attempting to address the above issue would lead to better controller design methods for active magnetic bearing systems
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